Large solutions, metasolutions, and asymptotic behaviour of the
regular positive solutions of sublinear parabolic problems

Julian Lopez-Gomez
Abstract:
In this paper we analyze the existence of regular and large
positive solutions for a class of non-linear elliptic boundary
value problems of logistic type in the presence of refuges. These
solutions describe the asymptotic behaviour of the regular
positive solutions of the associated parabolic model. The main
tool in our analysis is an extension of the interior estimates
found by J. B. Keller and R. Osserman
to cover the case of changing sign nonlinearities
combined with the construction of adequate sub and supersolutions.
The supersolutions are far from obvious since the nonlinearity
vanishes in finitely many regions of the underlying support
domain.